Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

A linear second order unconditionally maximum bound principle-preserving scheme for the Allen-Cahn equation with general mobility

Dianming Hou, Tianxiang Zhang and Hongyi Zhu
Applied Numerical Mathematics 207 222 (2025)
https://doi.org/10.1016/j.apnum.2024.09.005

Convergence and stability analysis of energy stable and bound‐preserving numerical schemes for binary fluid‐surfactant phase‐field equations

Jiayi Duan, Xiao Li and Zhonghua Qiao
Numerical Methods for Partial Differential Equations 40 (6) (2024)
https://doi.org/10.1002/num.23125

An Exponential Time Differencing Runge–Kutta Method ETDRK32 for Phase Field Models

Weichen Cao, Hengli Yang and Wenbin Chen
Journal of Scientific Computing 99 (1) (2024)
https://doi.org/10.1007/s10915-024-02474-9

Maximum bound principle and non-negativity preserving ETD schemes for a phase field model of prostate cancer growth with treatment

Qiumei Huang, Zhonghua Qiao and Huiting Yang
Computer Methods in Applied Mechanics and Engineering 426 116981 (2024)
https://doi.org/10.1016/j.cma.2024.116981

A Second-Order Exponential Time Differencing Multi-step Energy Stable Scheme for Swift–Hohenberg Equation with Quadratic–Cubic Nonlinear Term

Ming Cui, Yiyi Niu and Zhen Xu
Journal of Scientific Computing 99 (1) (2024)
https://doi.org/10.1007/s10915-024-02490-9

Mathematical modeling and numerical simulation of the N-component Cahn-Hilliard model on evolving surfaces

Lulu Liu, Shijie Huang, Xufeng Xiao and Xinlong Feng
Journal of Computational Physics 513 113189 (2024)
https://doi.org/10.1016/j.jcp.2024.113189

An operator splitting scheme for numerical simulation of spinodal decomposition and microstructure evolution of binary alloys

Abdullah Shah, Sana Ayub, Muhammad Sohaib, Sadia Saeed, Saher Akmal Khan, Suhail Abbas and Said Karim Shah
Heliyon 9 (6) e16597 (2023)
https://doi.org/10.1016/j.heliyon.2023.e16597

A Positivity-Preserving, Energy Stable BDF2 Scheme with Variable Steps for the Cahn–Hilliard Equation with Logarithmic Potential

Qianqian Liu, Jianyu Jing, Maoqin Yuan and Wenbin Chen
Journal of Scientific Computing 95 (2) (2023)
https://doi.org/10.1007/s10915-023-02163-z

A linear second-order maximum bound principle-preserving BDF scheme for the Allen-Cahn equation with a general mobility

Dianming Hou, Lili Ju and Zhonghua Qiao
Mathematics of Computation 92 (344) 2515 (2023)
https://doi.org/10.1090/mcom/3843

Operator splitting based structure-preserving numerical schemes for the mass-conserving convective Allen-Cahn equation

Rihui Lan, Jingwei Li, Yongyong Cai and Lili Ju
Journal of Computational Physics 472 111695 (2023)
https://doi.org/10.1016/j.jcp.2022.111695

A family of structure-preserving exponential time differencing Runge–Kutta schemes for the viscous Cahn–Hilliard equation

Jingwei Sun, Hong Zhang, Xu Qian and Songhe Song
Journal of Computational Physics 492 112414 (2023)
https://doi.org/10.1016/j.jcp.2023.112414

Second-Order Semi-Lagrangian Exponential Time Differencing Method with Enhanced Error Estimate for the Convective Allen–Cahn Equation

Jingwei Li, Rihui Lan, Yongyong Cai, Lili Ju and Xiaoqiang Wang
Journal of Scientific Computing 97 (1) (2023)
https://doi.org/10.1007/s10915-023-02316-0

An energy stable linear BDF2 scheme with variable time-steps for the molecular beam epitaxial model without slope selection

Yuanyuan Kang, Hong-lin Liao and Jindi Wang
Communications in Nonlinear Science and Numerical Simulation 118 107047 (2023)
https://doi.org/10.1016/j.cnsns.2022.107047

A provably efficient monotonic-decreasing algorithm for shape optimization in Stokes flows by phase-field approaches

Futuan Li and Jiang Yang
Computer Methods in Applied Mechanics and Engineering 398 115195 (2022)
https://doi.org/10.1016/j.cma.2022.115195

A second order linear energy stable numerical method for the Cahn–Hilliard–Hele–Shaw system

Danxia Wang, Xingxing Wang and Hongen Jia
Journal of Computational and Applied Mathematics 403 113788 (2022)
https://doi.org/10.1016/j.cam.2021.113788

High order accurate in time, fourth order finite difference schemes for the harmonic mapping flow

Zeyu Xia, Cheng Wang, Liwei Xu and Zhengru Zhang
Journal of Computational and Applied Mathematics 401 113766 (2022)
https://doi.org/10.1016/j.cam.2021.113766

Phase field modeling and computation of multi-component droplet evaporation

Junxiang Yang
Computer Methods in Applied Mechanics and Engineering 401 115675 (2022)
https://doi.org/10.1016/j.cma.2022.115675

An explicit conservative Saul’yev scheme for the Cahn–Hilliard equation

Junxiang Yang, Yibao Li, Chaeyoung Lee, et al.
International Journal of Mechanical Sciences 217 106985 (2022)
https://doi.org/10.1016/j.ijmecsci.2021.106985

Energy Stability of BDF Methods up to Fifth-Order for the Molecular Beam Epitaxial Model Without Slope Selection

Yuanyuan Kang and Hong-lin Liao
Journal of Scientific Computing 91 (2) (2022)
https://doi.org/10.1007/s10915-022-01830-x

On novel linear schemes for the Cahn–Hilliard equation based on an improved invariant energy quadratization approach

Rui Chen and Shuting Gu
Journal of Computational and Applied Mathematics 414 114405 (2022)
https://doi.org/10.1016/j.cam.2022.114405

Error Estimate of Exponential Time Differencing Runge-Kutta Scheme for the Epitaxial Growth Model Without Slope Selection

Yabing Sun and Quan Zhou
Journal of Scientific Computing 93 (1) (2022)
https://doi.org/10.1007/s10915-022-01977-7

An accurate and parallel method with post-processing boundedness control for solving the anisotropic phase-field dendritic crystal growth model

Yan Wang, Xufeng Xiao and Xinlong Feng
Communications in Nonlinear Science and Numerical Simulation 115 106717 (2022)
https://doi.org/10.1016/j.cnsns.2022.106717

A new symmetric linearly implicit exponential integrator preserving polynomial invariants or Lyapunov functions for conservative or dissipative systems

Lu Li
Journal of Computational Physics 449 110800 (2022)
https://doi.org/10.1016/j.jcp.2021.110800

Numerical investigation into the dependence of the Allen–Cahn equation on the free energy

Yunho Kim and Dongsun Lee
Advances in Computational Mathematics 48 (3) (2022)
https://doi.org/10.1007/s10444-022-09955-1

Unconditionally stable exponential time differencing schemes for the mass‐conserving Allen–Cahn equation with nonlocal and local effects

Kun Jiang, Lili Ju, Jingwei Li and Xiao Li
Numerical Methods for Partial Differential Equations 38 (6) 1636 (2022)
https://doi.org/10.1002/num.22827

A general class of linear unconditionally energy stable schemes for the gradient flows

Zengqiang Tan and Huazhong Tang
Journal of Computational Physics 464 111372 (2022)
https://doi.org/10.1016/j.jcp.2022.111372

A Second Order Accurate Scalar Auxiliary Variable (SAV) Numerical Method for the Square Phase Field Crystal Equation

Min Wang, Qiumei Huang and Cheng Wang
Journal of Scientific Computing 88 (2) (2021)
https://doi.org/10.1007/s10915-021-01487-y

Tikhonov Regularization Terms for Accelerating Inertial Mann-Like Algorithm with Applications

Hasanen A. Hammad, Habib ur Rehman and Hassan Almusawa
Symmetry 13 (4) 554 (2021)
https://doi.org/10.3390/sym13040554

Convergence analysis of Fourier pseudo-spectral schemes for three-dimensional incompressible Navier-Stokes equations

Cheng Wang
Electronic Research Archive 29 (5) 2915 (2021)
https://doi.org/10.3934/era.2021019

Energy Stable Numerical Schemes for Ternary Cahn-Hilliard System

Wenbin Chen, Cheng Wang, Shufen Wang, Xiaoming Wang and Steven M. Wise
Journal of Scientific Computing 84 (2) (2020)
https://doi.org/10.1007/s10915-020-01276-z

Energy stable higher-order linear ETD multi-step methods for gradient flows: application to thin film epitaxy

Wenbin Chen, Weijia Li, Cheng Wang, Shufen Wang and Xiaoming Wang
Research in the Mathematical Sciences 7 (3) (2020)
https://doi.org/10.1007/s40687-020-00212-9

The operator splitting method with semi-implicit spectral deferred correction for molecular beam epitaxial growth models

Zhifeng Weng, Yuping Zeng and Shuying Zhai
Journal of Algorithms & Computational Technology 14 (2020)
https://doi.org/10.1177/1748302620962352